RUBIN, J.

Sarah M. Unger, Boston, for the defendant.

Philip A. Mallard, Assistant District Attorney (Katelyn M. Giliberti, Assistant District Attorney, with him) for the Commonwealth.

Present: GREEN, RUBIN, & SULLIVAN, JJ.

RUBIN, J.The defendant was convicted under the animal cruelty statute for starving to death her dog, Arthur, a miniature dachshund. The finding of guilt is affirmed, as is the condition of the defendant's probation prohibiting her from owning “any pet or animal of any kind.” Under settled law, however, the condition of probation requiring the defendant to submit to suspicionless inspections of her home requires modification for which that aspect of the case will be remanded.

Facts. We recite the facts as they could have been found by the judge, the fact finder in this trial, viewing the evidence and all reasonable inferences therefrom in the light most favorable to the Commonwealth.

1. Arthur. On the night of January 23, 2013, the defendant brought Arthur to the Massachusetts Veterinary Referral Hospital in Woburn. Arthur was nonresponsive and was brought immediately to the treatment area for emergency care. He was seen by Christina Valiant, an emergency care veterinarian.

Dr. Valiant found Arthur in an extremely emaciated condition. She testified that he was “very, very, very thin”; that “his bones were all visible through his skin”; and that “he had no muscle mass.” He had physical indications of prolonged malnutrition: “a lot of the fur was rubbed away from the left side of his body.” Dr. Valiant also testified that Arthur “had scabs over the left side of his body where the fur had been rubbed away on the left side of his rib cage, on his elbow, on his knee, ... on [his] hip,” on the “tip of his tail,” and on the “tip[s] of his ears.” Dr. Valiant testified that scabs and “pressure sores” come from “laying on one particular part of the body and not moving” because the “compression of the skin for a long enough period of time” causes the skin “to necrose or die” and “the sores result[ ].” The sores and scabs on Arthur indicated that he “had been laying on the left side of his body and not getting up and moving around and keeping himself off of those areas.” A blood test showed that he was dehydrated.

When Arthur arrived at the hospital he was “mostly dead” and his vital signs were bleak: he was not moving at all, “not breathing,” “unresponsive to stimuli,” “cold to the touch,” and “barely” had a heartbeat. Particularly concerning were his “fixed [and] dilated pupils” and the absence of “a palpable reflex” and a “corneal reflex,” the latter absence being a sign of brain stem damage. Arthur had no other “obvious abnormalities.” An “oral exam was normal” and there were no discernible “abnormalities in his abdomen.”

As soon as Dr. Valiant saw Arthur's condition, she and the triage nurse started cardiopulmonary resuscitation (CPR); they tried to revive him for about twenty minutes. In Dr. Valiant's view at the time, “even if [she was] able to resuscitate him and get him breathing again,” she “didn't think that he was ever going to regain consciousness.”

After twenty minutes of CPR without response, the defendant authorized euthanasia and Arthur was euthanized.

2. The defendant's statements at the hospital. When Dr. Valiant asked the defendant at the hospital what was going on with Arthur and how long he had been as he was, she claimed that he had “always been a thin dog,” and that “she had noticed for the last week or so that he had lost some more weight.” The defendant also said he “had been coughing for a week before” the visit. She said that she had not “observed any vomiting, diarrhea, or loose stools.” She claimed that Arthur “hadn't seemed quite right” the day before, and that he “was just sort of laying there and staring ... off into [the] distance.” She claimed that he “did eat and drink a little the day before,” but that day she “had been gone at work all day” and “when she came home she found him just lying there.” She mentioned that she “had never brought [Arthur] to a veterinarian.” Dr. Valiant testified that while talking with her, the defendant “was fairly calm” and “didn't seem terrifically upset about anything.”

3. Dr. Valiant's opinion testimony. On direct examination, the prosecutor asked Dr. Valiant to “estimate how long it had taken for Arthur to get to that point.” She explained that in accordance with a “Colorado State” study from the 1970s, it generally takes “approximately four to six weeks of complete starvation” for a pet to develop “from an ideal body condition to an emaciated body condition.” Because Arthur was so thin, Dr. Valiant believed he “had been like that for ... a long time.” She stated that Arthur “[a]bsolutely” would have experienced pain, given his state. On cross-examination Dr. Valiant testified that Arthur died of starvation. She testified that there were no overt indications of other causes, and she explicitly excluded some other possible causes of death. On redirect, she opined that Arthur was “thin enough that you would think that it was impossible for him to have gotten into that condition in a period of a week's time,” as the defendant had told her.

4. The necropsy. Because Dr. Valiant disbelieved the defendant's story, she preserved Arthur's body and contacted the Massachusetts Society for the Prevention of Cruelty to Animals (MSPCA). Martha Parkhurst, a sergeant in the law enforcement department at the MSPCA, was assigned to the case and interviewed the defendant. She learned that the defendant was employed and described the defendant's apartment as “neat and clean.”

The defendant told Parkhurst that she had acquired Arthur “a few years before,” that her normal routine with him was to feed him twice a day, and that she had not noticed his weight loss until a couple of days before she took him to the veterinarian. She said that Arthur “had been eating and drinking normally and then lost a lot of weight all of a sudden.” However, she had not noticed the weight loss on January 20, when her son gave Arthur a bath, although she did notice a sore on his elbow. According to the defendant, Arthur had not eaten very much in the morning of January 23 and, when the defendant came home, he was lying in his crate, did not eat or drink, and needed help standing up.

Parkhurst took Arthur's body to Dr. Pamela Mouser at the Angell Animal Medical Center and she conducted a necropsy. Dr. Mouser testified that in cases of suspected neglect, a necropsy includes a search for any underlying disease process that could mimic the evidence of neglect. In cases of suspected malnourishment, the necropsy focuses on whether the animal can eat, whether there is any reason the animal was unable to absorb nutrients through the gut, and whether the animal had diarrhea. During the necropsy, the doctor looks for fat in the chest and abdominal cavities, which are the places where the animal would lose fat last, and at muscle mass, as the body will use muscle for energy “once all of the [fat] is used up.”

Dr. Mouser's necropsy report was introduced in evidence. The report concluded that the “[g]ross findings, including absence of body fat stores and marked loss of skeletal muscle mass, support a diagnosis of emaciation.... An underlying disease process which might have contributed to this marked loss of condition, or which might have caused a rapid loss of condition over a short period of time, is not identified.... The patient had partially-digestedd kibble within the stomach, indicative of an ability to prehend and swallow food. In addition, the colon contained soft-formed feces without evidence of diarrhea.” The report also stated that “[t]he inciting cause of the skin wounds is not definitively determined. Given [that] the majority of skin lesions are distributed on the left side, pressure sores (as suspected clinically) from prolonged recumbency on that side would have to be considered. Regardless of the cause, all examined skin wounds have evidence of bacterial infection.”

Dr. Mouser opined that Arthur died of severe malnourishment. She concluded that there was no other disease that caused the emaciated state of Arthur's body. Arthur was able to chew and swallow food and could eat if offered it.

Dr. Mouser concluded that this malnourishment was caused by Arthur not getting enough food. She testified that if Arthur was getting no food, it would have taken a matter of weeks for him to get to the condition he was in at death, and that if he was getting any food at all, it would have taken longer. She opined that Arthur's sores would have been painful and that Arthur would have suffered “the pain and the anxiety of being hungry.”

After a bench trial, the defendant was convicted of animal cruelty, in violation of G.L. c. 272, § 77, as amended by St. 1984, c. 50, which provides, in relevant part, that “[w]hoever ... deprives of necessary sustenance ... or kills an animal ...; and whoever, having the charge or custody of an animal, either as owner or otherwise, inflicts unnecessary cruelty upon it, or unnecessarily fails to provide it with proper food, drink, shelter, sanitary environment, or protection from the weather ... shall be punished.” She was sentenced to two and one-half years in the house of correction, suspended for five years, mandatory supervised probation, and 500 hours of community service. As conditions of probation, she was not to have “any pet or animal of any kind at any time during th[e] probationary period” and her home was “to be open for mandatory random inspections by [the] MSPCA and/or the probation department.” She now appeals.

Discussion. The defendant argues that the animal cruelty statute under which she was convicted is unconstitutionally vague; that the Commonwealth's expert witnesses, Drs. Valiant and Mouser, gave improper testimony; that there was insufficient evidence to support her conviction; that she may not as a condition of probation be prohibited from owning animals; and that the condition of probation allowing suspicionless searches of her property must be modified. We address each argument in turn. 1. Vagueness of the word “animal.” The defendant argues that G.L. c. 272, § 77, is unconstitutionally vague because it does not contain a definition of the word “animal.”

This challenge is easily dispensed with. As the defendant acknowledges, imprecision in a law's outer boundaries “does not permit a facial attack on the entire law by one whose conduct ‘falls squarely within the “hard core” of the [law's] proscriptions.’ ” Chief of Police of Worcester v. Holden, 470 Mass. 845, 860, 26 N.E.3d 715 (2015), quoting from Commonwealth v. Orlando, 371 Mass. 732, 734, 359 N.E.2d 310 (1977). This rule applies with particular force in cases, like this one, where any potential vagueness in the outer boundaries of the law is not going to chill protected expression. See Commonwealth v. Casey, 42 Mass.App.Ct. 512, 516 n. 4, 678 N.E.2d 436 (1997), quoting from Commonwealth v. Adams, 389 Mass. 265, 271, 450 N.E.2d 149 (1983) (“[I]n evaluating a statute which does not implicate First Amendment freedoms it is a well established principle that vagueness challenges must be evaluated in light of the facts of the case at hand”).

We have no trouble concluding that dogs are animals within the meaning of the word “animal,” and within the meaning of that word in the statute, and that protecting dogs comes within the hard core of the law's prohibition on starving animals in one's custody. Indeed, our appellate courts have previously upheld convictions related to cruelty to dogs. See Commonwealth v. Erickson, 74 Mass.App.Ct. 172, 176–178, 905 N.E.2d 127 (2009) ; Commonwealth v. Zalesky, 74 Mass.App.Ct. 908, 909, 906 N.E.2d 349 (2009). See also Commonwealth v. Turner, 145 Mass. 296, 300, 14 N.E. 130 (1887) (captive fox is an “animal” under earlier version of statute). The fact that none of the animals was a miniature dachshund, a distinction raised before us at oral argument, makes no difference. All dogs are animals regardless of breed.

2. Expert testimony. The defendant contends that it was improper for Dr. Valiant to estimate based on her training and experience how long it had taken Arthur to reach the condition he was in because the answer was speculative. In particular, the defendant argues that it was error to permit Dr. Valiant to testify that Arthur was “thin enough that you would think that it was impossible for him to have gotten into that condition in a period of a week's time[,] which [the defendant] told me” and that he “had been like that for such a long time,” because there was no evidence of his body weight at any time prior to the necropsy.

“A judge has broad discretion regarding the admission of expert testimony, and we review that decision only for abuse of discretion.” Commonwealth v. Robinson, 449 Mass. 1, 5, 864 N.E.2d 1186 (2007). “The test [in deciding whether to admit expert testimony] is whether the testimony ‘will assist the trier of fact to understand the evidence or to determine a fact in issue.’ ” Commonwealth v. Torres, 469 Mass. 398, 406, 14 N.E.3d 253 (2014), quoting from Mass. G. Evid. § 702 (2014). The defendant did not object to these statements, and so we review for whether any error created a substantial risk of a miscarriage of justice. We think the testimony was properly admitted. Dr. Valiant's opinion that “you would think that it was impossible for [Arthur] to have gotten into that condition in a period of a week's time[,] which [the defendant] told me” was not merely speculation. Dr. Valiant testified that she observed Arthur at the time of his death and concluded that “[h]e was in an emaciated body condition.” The defendant's account of the events leading to Arthur's death was that he had been eating and drinking normally and then suddenly lost weight and died over the course of one week. It was not speculation for Dr. Valiant to opine, essentially, that Arthur's condition at the time of his death was inconsistent with a single week of malnourishment. See id. at 407, 14 N.E.3d 253 (“An expert opinion that is not definitive but expressed in terms of observations being ‘consistent with’ a particular cause, or words of similar effect, does not render the opinion inadmissible on the ground that it is ‘speculative’ ” [citation omitted] ).

Dr. Valiant's opinion that Arthur “had been like that for such a long time” was also not merely speculation. Dr. Valiant already had testified that pressure sores, such as those she observed on Arthur, occur only “when there's compression of the skin for a long enough period of time.” In addition, there was no risk that Dr. Valiant's opinions misled the fact finder. At the time she expressed these opinions, she already had made clear the limitations on her ability to come to a precise conclusion. She acknowledged that “[i]t's hard to estimate completely accurately [how long it had taken for Arthur to get to the state he was in] because [she had] never examined him before.” In the circumstances, the imprecision in her opinions because of factors unknown to her goes to their weight, not their admissibility. Sacco v. Roupenian, 409 Mass. 25, 29–30, 564 N.E.2d 386 (1990), quoting from Baker v. Commercial Union Ins. Co., 382 Mass. 347, 351, 416 N.E.2d 187 (1981) (“So long as the facts on which the doctor's opinion is based are in evidence, ‘[t]he question whether the basis of the doctor's opinion is sound goes to the weight of the evidence, not its admissibility’ ”).

The defendant also argues that the reference to the Colorado State study was error, and we agree. An expert may rely on inadmissible hearsay, but she may not testify to its contents on direct examination. See Commonwealth v. Greineder, 464 Mass. 580, 584, 984 N.E.2d 804 (2013) (“In Massachusetts, we draw a distinction between an expert's opinion on the one hand and the hearsay information that formed the basis of the opinion on the other, holding the former admissible and the latter inadmissible”). See also Vassallo v. Baxter Healthcare Corp., 428 Mass. 1, 16, 696 N.E.2d 909 (1998). Nonetheless, even assuming the claim of error was preserved, we see no prejudice flowing from the mention of this unnamed study. Given Dr. Valiant's credentials and the other bases for her opinions that already had been admitted in evidence, we do not think the strength of her opinion turned on the precise study to which she referred.

The defendant next complains of Dr. Mouser's testimony, to which she did not object, about how long it took Arthur to become emaciated. She claims that without knowing Arthur's body weight at some point before his death, any opinion by Dr. Mouser was speculative. Dr. Mouser, however, made clear that the precise length of time depended on body weight and that without knowing it, and how much food Arthur was receiving, she could only estimate. Nonetheless, that does not render her estimate speculative. See Commonwealth v. Torres, 469 Mass. at 407, 14 N.E.3d 253.

Finally, the defendant complains that the unobjected—to testimony opining that the defendant starved Arthur to death was speculative and conjectural. But these were opinions of veterinarians, one of whom examined Arthur, and one of whom performed his necropsy. Both witnesses' opinions were based on their observations of Arthur's body, their inquiries into other possible causes, and their training and experience. Their opinions were adequately supported.

3. Sufficiency of the evidence. In her last challenge to the finding the defendant argues that the evidence was insufficient to support her conviction. She assumes she was convicted under that branch of the statute prohibiting “unnecessarily fail[ing] to provide [the animal] with proper food.” Even assuming she is correct, there is no merit to her claim. The inferences that support a conviction “need only be reasonable and possible; [they] need not be necessary or inescapable.” Commonwealth v. Woods, 466 Mass. 707, 713, 1 N.E.3d 762 (2014), quoting from Commonwealth v. Merola, 405 Mass. 529, 533, 542 N.E.2d 249 (1989). As to failure to provide food, the defendant posits other possible ways Arthur might have starved, such as a disease that made him unable to eat or a parasite. But there was sufficient evidence from which the judge could have concluded that that is not what happened. The judge was entitled to credit the expert opinions that Arthur died from starvation, and not from any underlying disease. These opinions were supported by evidence that Arthur still was able to eat and to digest food at the time of his death, and that a “vast majority” of other possible causes of his condition had been ruled out. The defendant also argues that any failure to feed Arthur may not have been unnecessary—but in light of the defendant's own statements to Dr. Valiant and the MSPCA investigator, the judge as the finder of fact was entitled to conclude that it was.

4. Conditions of probation. The defendant complains about two conditions of her probation. First, she argues that the prohibition on having “a pet or animal of any kind” during her probation violates her fundamental constitutional right to own property. See art. 1 of the Declaration of Rights of the Massachusetts Constitution. We need not and do not decide in this case whether there is a fundamental constitutional right to possess or to care for an animal because so long as a condition of probation bears a reasonable relationship to “the goals of sentencing and probation,” which include “rehabilitation of the probationer,” “protection of the public,” “punishment,” “deterrence,” and “retribution,” it is permissible even when it impairs a fundamental constitutional right. Commonwealth v. Pike, 428 Mass. 393, 403, 701 N.E.2d 951 (1998). Indeed, those convicted of felonies are prohibited ever from owning a firearm notwithstanding the constitutional right to bear arms protected by the Second Amendment to the United States Constitution. See 18 U.S.C. § 922(g) (2012) ; District of Columbia v. Heller, 554 U.S. 570, 595, 128 S.Ct. 2783, 171 L.Ed.2d 637 (2008). In light of the conduct underlying the defendant's conviction, there is nothing improper about prohibiting her from having a pet or an animal of any kind as a condition of her probation.

Finally, the defendant argues that the condition of probation ordering that her home “be open for mandatory random inspections by [the] MSPCA and/or the probation department” violates her right to be secure from unreasonable searches under art. 14 of the Declaration of Rights of the Massachusetts Constitution. In particular, she argues that this condition impermissibly authorizes searches of her home without reasonable suspicion and without a warrant.

She is correct. Under art. 14, “a reduced level of suspicion, such as ‘reasonable suspicion,’ will justify a search of a probationer and her premises,” but “any standard below ... reasonable suspicion” will not. Commonwealth v. LaFrance, 402 Mass. 789, 792, 793, 525 N.E.2d 379 (1988). In addition, a warrant still is required for a search of a probationer's home, “barring the appropriate application of a traditional exception to the warrant requirement.” Id. at 794, 525 N.E.2d 379. See Commonwealth v. Duncan, 467 Mass. 746, 747, 7 N.E.3d 469 (2014)“[I]n appropriate circumstances, animals, like humans, should be afforded the protection of the emergency aid exception [to the warrant requirement]”); Commonwealth v. Moore, 473 Mass. 481, 487, 43 N.E.3d 294 (2016) (“This interpretation [in LaFrance ] remains the standard for probationer searches under art. 14 ”).

The defendant's probationary conditions therefore must be modified so that the defendant will be subject to searches by the MSPCA and the probation department only upon reasonable suspicion and only pursuant to a warrant or a traditional exception to the warrant requirement. Conclusion. The finding of guilt of animal cruelty is affirmed. The condition of probation requiring the defendant to submit to random inspections of her home is vacated, and the case is remanded to the District Court for modification of that probationary term consistent with this opinion. All other terms and conditions of the defendant's sentence remain valid and unchanged.

So ordered.